Answer:
No, a blood test could not eliminate the father.
Step-by-step explanation:
The mother had B type blood, so the possible genotypes are BB and BI. The father had A type blood, so the possible genotypes are AA and AI. The child had O type blood, so the only possible genotype is II. If the mother has the genotype BI and the father has the genotype AI, then there is a 25% chance the child will have the blood type O, or II (I used a punnet square with the genotypes BI and AI to solve this.)